Intermediate Algebra (6th Edition)

by
Martin-Gay, Elayn

Published by
Pearson

ISBN 10:
0321785045

ISBN 13:
978-0-32178-504-6

Chapter 5 - Section 5.6 - Factoring Trinomials - Exercise Set: 8

Answer

$(x+3)(x-12)$

Work Step by Step

In order to factor $x^{2}-9x-36$, we must find a pair of numbers whose product is equal to -36 (or the constant term) and whose sum is equal to -9 (or the coefficient on the middle term). We know that only a pair of one positive and one negative number will produce a negative product and a negative sum.
We know that the pairs of numbers whose product is -36 are -1,36, 1,-36, -2,18, 2,-18, -3,12, 3,-12, -4,9, 4,-9, and 6,-6.
Out of these pairs, the sum of 3 and -12 is equal to -9.
Therefore, $x^{2}-9x-36=(x+3)(x-12)$.